Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Criminal career-related factors among female robbers in the State of Sao Paulo, Brazil, and a presumed 'revolving-door' situation

Introduction: Risk-taking behaviors, family criminality, poverty, and poor parenting have been frequently associated with an earlier onset of criminal activities and a longer criminal career among male convicts. Objective: This study aims to identify factors related to the onset and recurrence of criminal behavior among female robbers in the State of Sao Paulo - Brazil. Method: It was a cross-sectional study carried out inside a feminine penitentiary in Sao Paulo. From June 2006 to June 2010, 175 inmates convicted only for robbery were recruited to be evaluated about family antecedents of criminal conviction, alcohol and drug misuse, impulsiveness, depressive symptoms, and psychosocial features. Results: Having family antecedents of criminal conviction consistently predicted an earlier onset of criminal activities and a longer criminal career among female robbers. Drug use in youth and the severity of drug misuse were significantly related to the initiation and recurrence of criminal behavior, respectively. Discussion: Prisons must systematically screen detainees and provide treatments for those with health problems in general. Children of inmates should obtain help to modify the negative consequences of their parents' incarceration in order to mitigate the negative consequences of pursuing this 'static' factor.